Finite Group Databasebeta

← #11866189

Subgroups — #11866189

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595223C211yesmaximal, characteristic, complemented
3#10595168C211yesmaximal, characteristic, complemented
4C2×#63937C211yesmaximal, characteristic, complemented
5C3×#5153C211yesmaximal, characteristic, complemented
6C3×#5150C211yesmaximal, characteristic, complemented
7#10591481C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10591432C211yesmaximal, characteristic, complemented
10#10591429C211yesmaximal, characteristic, complemented
11#10591426C211yesmaximal, characteristic, complemented
12#10590956C211yesmaximal, characteristic, complemented
13#10590770C211yesmaximal, characteristic, complemented
14#10590765C211yesmaximal, characteristic, complemented
15#10590701C211yesmaximal, characteristic, complemented
16#80536—31nomaximal
17#80334—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24D8×C3⋊D3—24no—
25C2×#3745C2211yescharacteristic
26C2×C8×C3⋊D3C2211yescharacteristic
27C3×#940C2211yescharacteristic, complemented
28C3×#936C2211yescharacteristic, complemented
29C3×D4×Dic3C2211yescharacteristic, complemented
30C3×D4×Dic3C2211yescharacteristic, complemented
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33#63981—21no—
34#63981—21no—
35#63974—21no—
36#63971—21no—
37#63971—21no—
38C2×#3722—21no—
39#63952—21no—
40#63952—21no—
41#63937—24no—
42#63911C2211yescharacteristic, complemented
43#63894C2211yescharacteristic, complemented
44#63894C2211yescharacteristic, complemented
45#63874C2211yescharacteristic
46#63864C2211yescharacteristic, complemented
47#63849C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3712C2211yescharacteristic
51C3×#832C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C2×D3×D8—61no—
68#5715—31no—
69#5674—31no—
70#5545—31no—
71#5545—31no—
72C3×#463—31no—
73C3×#459—31no—
74#5165—31no—
75#5153D311yescharacteristic, complemented
76#5150—31no—
77#5150D311yescharacteristic, complemented
78#5072—31no—
79#5057—31no—
80#5016—31no—
81#5015—31no—
82#4844—31no—
83#4843—31no—
84#4839—31no—
85#4839—31no—
86#4819—31no—
87#4804—31no—
88#4787—31no—
89#4786—31no—
90#4786—31no—
91#4772—31no—
92#4770—31no—
93#4770—31no—
94C23×C3⋊D3—21no—
95C23×C3⋊D3—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3—22no—
103D4×C3⋊D3D414yescomplemented
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#624—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119#3796—22no—
120#3796—22no—
121C32×D8—22no—
122C2×C32×C8C2311yescharacteristic
123#3753—22no—
124#3753—22no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3745—22no—
127C8×C3⋊D3—22no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#214—22no—
133C3×#213—22no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140#3724D411yescharacteristic
141#3724D411yescharacteristic
142#3722—21no—
143#3722—21no—
144#3722—21no—
145#3722—21no—
146#3722—21no—
147#3722D411yescharacteristic
148#3722D411yescharacteristic
149Dic32—21no—
150#3717—22no—
151#3714—22no—
152#3712—22no—
153#3041—91noSylow
154C2×#239—31no—
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C2×C3×SD16—31no—
163C2×C3×D8—21no—
164C2×C3×D8—31no—
165C2×C3×D8C2×D311yescharacteristic
166C2×C3×D8C2×D311yescharacteristic
167C3×#127—31no—
168C3×#124—31no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171#947—31no—
172C2×#215—31no—
173#940—31no—
174#940C2×D311yescharacteristic, complemented
175#939—61no—
176#939—61no—
177#937—61no—
178#937—61no—
179#936C2×D311yescharacteristic, complemented
180D4×Dic3C2×D311yescharacteristic, complemented
181D4×Dic3C2×D311yescharacteristic, complemented
182C2×#214C2×D311yescharacteristic, complemented
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—61no—
189C2×#213—61no—
190C2×#213C2×D311yescharacteristic, complemented
191C4×#67—61no—
192C4×#67—61no—
193C2×(C2×D3)⋊C4—61no—
194C2×(C2×D3)⋊C4—61no—
195#914—64no—
196#911—64no—
197D3×D8—64no—
198D3×D8—64no—
199D3×D8—68no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—61no—
204C2×#204—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—31no—
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—61no—
210#893—31no—
211#893—31no—
212#892—31no—
213#892—31no—
214#884—61no—
215#884—61no—
216#882—61no—
217#882—61no—
218#67⋊C4—61no—
219#67⋊C4—61no—
220D3×C22⋊C4—61no—
221D3×C22⋊C4—61no—
222#875—31no—
223#874—31no—
224C4×D12—31no—
225C4×D12—31no—
226#872—31no—
227#872—31no—
228C3×C4⋊C8—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102—31no—
234#835—31no—
235#832—31no—
236#832C2×D311yescharacteristic, complemented
237#832C2×D311yescharacteristic, complemented
238#821—31no—
239#821—31no—
240#821C2×D311yescharacteristic, complemented
241#816C2×D311yescharacteristic, complemented
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8C2×D311yescharacteristic, complemented
245Dic3⋊C8C2×D311yescharacteristic, complemented
246#810—31no—
247#809—31no—
248#809—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C23×C32—21no—
253C23×C32—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—24no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—81no—
259C22×C3⋊D3—81no—
260C22×C3⋊D3—81no—
261C22×C3⋊D3—81no—
262C22×C3⋊D3C2×D411yescharacteristic
263C22×C3×D3—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4C2×D412yes—
268C2×C32×C4C2411yescharacteristic
269#638—24no—
270#638—42no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3C2×D412yes—
277C4×C3⋊D3#4112yes—
278C3×#67—81no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3—81no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#626—42no—
294#626—81no—
295#626—81no—
296#624—81no—
297#624—81no—
298D3×Dic3—42no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C22×D8—91no—
305#535—91no—
306#518—91no—
307#463—31no—
308#463—91no—
309#463—91no—
310#463—91no—
311#459—31no—
312#459—91no—
313#459—91no—
314#459—91no—
315#424—91no—
316#418—91no—
317#416—91no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3—61no—
322C23×D3—121no—
323C23×D3—121no—
324C2×C3×Q8—31no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—121no—
346C2×#67—121no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—61no—
350#239—62no—
351#239—62no—
352#237—62no—
353#237—62no—
354D3×D4—34no—
355D3×D4—34no—
356D3×D4—64no—
357D3×D4—62no—
358D3×D4—62no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—64no—
364D3×D4—122no—
365D3×D4—122no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—31no—
377C2×C4×D3—31no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×Dic6C22×D311yescharacteristic
385C3×SD16—62no—
386C3×D8—24no—
387C3×D8—22no—
388C3×D8—22no—
389C3×D8—62no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C42—31no—
402C3×C42—31no—
403#217—21no—
404#217—21no—
405#217—21no—
406#217—21no—
407#215—62no—
408#214—22no—
409#213—22no—
410#213—62no—
411#213—62no—
412#213—62no—
413#213—64no—
414#213—64no—
415#213—62no—
416#213—62no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431C4⋊Dic3C22×D311yescharacteristic
432C4⋊Dic3C22×D311yescharacteristic
433Dic3⋊C4—31no—
434Dic3⋊C4—31no—
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
437C4×Dic3—61no—
438C4×Dic3—61no—
439C4×Dic3C22×D311yescharacteristic
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—62no—
447D24—62no—
448D24—64no—
449D24—62no—
450#204—62no—
451ΓL(1,𝔽25)—62no—
452ΓL(1,𝔽25)—62no—
453D3×C8—62no—
454D3×C8—62no—
455D3×C8—64no—
456C22×C32—22no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32C22×D411yescharacteristic
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—84no—
472C2×C3⋊D3—84no—
473C2×C3⋊D3#12112yes—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C32×C4C22×D411yescharacteristic
478C32×C4C2×#4111yescharacteristic
479C3⋊Dic3#12112yes—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C2×#41—91no—
488C22×D4—91no—
489C22×D4—91no—
490AGL(1,ℤ/8)—184no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×D8—31no—
494C2×D8—91no—
495C2×D8—91no—
496C2×D8—91no—
497C2×D8—91no—
498C2×D8—184no—
499C2×D8D3211yescharacteristic
500C2×M16—91no—
501C22×C8—91no—
502#127—31no—
503#127—91no—
504#124—31no—
505#124—91no—
506#121—181no—
507#121—181no—
508#120—181no—
509#120—181no—
510C4×D4—31no—
511C4×D4—31no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—181no—
515C4×D4—181no—
516#117—91no—
517#117—91no—
518C2×C22⋊C4—181no—
519C2×C22⋊C4—181no—
520C4⋊C8—31no—
521C4⋊C8—31no—
522C4⋊C8—91no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—31no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—61no—
539C22×D3—21no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—61no—
543C22×D3—64no—
544C22×D3—64no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—124no—
550C22×D3—121no—
551C22×D3—121no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—124no—
555C22×D3—241no—
556C22×D3—241no—
557C22×D3—241no—
558C22×D3—241no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—242no—
564C22×D3—242no—
565C22×D3—242no—
566C22×D3—242no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×D4—22no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—22no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—241no—
582C3×D4—241no—
583C3×D4D3×D412yes—
584C3×D4D3×D412yes—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—241no—
594C2×C3×C4—241no—
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—64no—
598#67—64no—
599#67—81no—
600#67—81no—
601#67—124no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—124no—
606#67—241no—
607#67—241no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—61no—
614C2×Dic3—81no—
615C2×Dic3—81no—
616C2×Dic3—122no—
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621D12—21no—
622D12—21no—
623D12—32no—
624D12—32no—
625D12—62no—
626D12—62no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—121no—
634D12—121no—
635D12—122no—
636D12—241no—
637D12—241no—
638C4×D3—32no—
639C4×D3—32no—
640C4×D3—32no—
641C4×D3—32no—
642C4×D3—62no—
643C4×D3—62no—
644C4×D3—122no—
645C4×D3—241no—
646C4×D3—241no—
647C4×D3—241no—
648C4×D3—241no—
649Dic6—21no—
650Dic6—21no—
651C3×C8—22no—
652C3×C8—21no—
653C3×C8—21no—
654C3×C8—61no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8—21no—
658C3⋊C8—62no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C2×C32—42no—
662C2×C32—81no—
663C2×C32C2×#12111yescharacteristic
664C2×C32#57611yescharacteristic
665C2×C32#57611yescharacteristic
666C3⋊D3—22no—
667C3⋊D3—42no—
668C3⋊D3—81no—
669C3×D3—81no—
670C24—181no—
671C24—181no—
672#41—182no—
673#41—182no—
674C2×Q8—31no—
675C2×D4—31no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—94no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—182no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4C2×D3211yescharacteristic
690C2×D4C2×D3211yescharacteristic
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—91no—
694C22×C4—181no—
695C22×C4—181no—
696C22×C4—181no—
697SD16—62no—
698SD16—182no—
699D8—22no—
700D8—62no—
701D8—182no—
702D8—182no—
703D8—182no—
704D8—182no—
705M16—182no—
706C2×C8—31no—
707C2×C8—31no—
708C2×C8—91no—
709C2×C8—182no—
710C2×C8C2×D3211yescharacteristic
711C4⋊C4—31no—
712C4⋊C4—31no—
713C4⋊C4—91no—
714C4⋊C4—91no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—91no—
720C22⋊C4—91no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C42—31no—
727C42—31no—
728C42—181no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C2×D3—32no—
754C2×D3—32no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—122no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—122no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—244no—
784C2×D3—244no—
785C2×D3—248no—
786C2×D3—248no—
787C2×D3—244no—
788C2×D3—244no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4—121no—
798C3×C4C2×D3×D411yescharacteristic
799C3×C4C2×D3×D411yescharacteristic
800C3×C4D3×#4111yescharacteristic
801C3×C4D3×#4111yescharacteristic
802Dic3—21no—
803Dic3—21no—
804Dic3—21no—
805Dic3—21no—
806Dic3—32no—
807Dic3—32no—
808Dic3—41no—
809Dic3—41no—
810Dic3—41no—
811Dic3—62no—
812C32#304111yescharacteristic, complemented, Sylow
813C23—21no—
814C23—21no—
815C23—61no—
816C23—91no—
817C23—184no—
818C23—181no—
819C23—181no—
820C23—362no—
821C23—721no—
822C23—721no—
823C23—721no—
824C23—721no—
825Q8—61no—
826Q8—61no—
827D4—21no—
828D4—21no—
829D4—21no—
830D4—61no—
831D4—61no—
832D4—92no—
833D4—184no—
834D4—181no—
835D4—181no—
836D4—181no—
837D4—241no—
838D4—241no—
839D4—362no—
840D4—362no—
841D4—721no—
842D4—721no—
843D4#381112yes—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—91no—
852C2×C4—92no—
853C2×C4—92no—
854C2×C4—241no—
855C2×C4—241no—
856C2×C4—362no—
857C2×C4—721no—
858C2×C4—721no—
859C2×C4C22×D3211yescharacteristic
860C8—21no—
861C8—61no—
862C8—61no—
863C8—181no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—42no—
868C2×C3—42no—
869C2×C3—82no—
870C2×C3—82no—
871C2×C3—81no—
872C2×C3—81no—
873C2×C3—241no—
874C2×C3D3×#12111yescharacteristic
875C2×C3D3×#12111yescharacteristic
876C2×C3#575711yescharacteristic
877C2×C3#576911yescharacteristic
878C2×C3#577411yescharacteristic
879C2×C3#577411yescharacteristic
880D3—64no—
881D3—62no—
882D3—62no—
883D3—81no—
884D3—122no—
885D3—122no—
886D3—242no—
887D3—242no—
888D3—241no—
889D3—241no—
890C22—22no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—92no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—181no—
901C22—181no—
902C22—182no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—724no—
909C22—724no—
910C22D32×D411yescharacteristic
911C4—61no—
912C4—61no—
913C4—61no—
914C4—61no—
915C4—92no—
916C4—121no—
917C4—121no—
918C4—121no—
919C4#6431211yescharacteristic
920C4C2×#381111yescharacteristic
921C3—21no—
922C3#8033411yescharacteristic, complemented
923C3#8053611yescharacteristic, complemented
924C2—42no—
925C2—81no—
926C2—182no—
927C2—241no—
928C2—362no—
929C2—721no—
930C2#1059473411yescharacteristic
931C2#1059473511yescharacteristic
932C2#1059529811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D8×C3⋊D3C2semidirect
2. #10595223C2semidirect
3. #10595168C2semidirect
4. C2×#63937C2semidirect
5. C3×#5153C2semidirect
6. C3×#5150C2semidirect
7. #10591481C2semidirect
8. #10591471C2semidirect
9. #10591432C2semidirect
10. #10591429C2semidirect
11. #10591426C2semidirect
12. #10590956C2semidirect
13. #10590770C2semidirect
14. #10590765C2semidirect
15. #10590701C2semidirect
27. C3×#940C22semidirect
28. C3×#936C22semidirect
29. C3×D4×Dic3C22semidirect
30. C3×D4×Dic3C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#213C22semidirect
42. #63911C22semidirect
43. #63894C22semidirect
44. #63894C22semidirect
46. #63864C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
51. C3×#832C22semidirect
52. C3×#832C22semidirect
53. C3×#821C22semidirect
54. C3×#816C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
75. #5153D3semidirect
77. #5150D3semidirect
103. D4×C3⋊D3D4semidirect
174. #940C2×D3semidirect
179. #936C2×D3semidirect
180. D4×Dic3C2×D3semidirect
181. D4×Dic3C2×D3semidirect
182. C2×#214C2×D3semidirect
190. C2×#213C2×D3semidirect
236. #832C2×D3semidirect
237. #832C2×D3semidirect
240. #821C2×D3semidirect
241. #816C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
245. Dic3⋊C8C2×D3semidirect
812. C32#3041semidirect
922. C3#80334semidirect
923. C3#80536semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D8×C3⋊D32
#105952232
#105951682
C2×#639372
C3×#51532
C3×#51502
#105914812
#105914712
#105914322
#105914292
#105914262
#105909562
#105907702
#105907652
#105907012
#805363
#803343